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Maximizing Revenue A charter flight charges a fare of $200
Chapter 2, Problem 54A(choose chapter or problem)
Problem 54A
Maximizing Revenue A charter flight charges a fare of $200 per person plus $4 per person for each unsold seat on the plane. The plane holds 100 passengers. Let x represent the number of unsold seats.
a. Find an expression for the total revenue received for the flight R(x). (Hint: Multiply the number of people flying, 100 − x, by the price per ticket.)
b. Graph the expression from part a.
c. Find the number of unsold seats that will produce the maximum revenue.
d. What is the maximum revenue?
e. Some managers might be concerned about the empty seats, arguing that it doesn’t make economic sense to leave any seats empty. Write a few sentences explaining why this is not necessarily so.
Questions & Answers
QUESTION:
Problem 54A
Maximizing Revenue A charter flight charges a fare of $200 per person plus $4 per person for each unsold seat on the plane. The plane holds 100 passengers. Let x represent the number of unsold seats.
a. Find an expression for the total revenue received for the flight R(x). (Hint: Multiply the number of people flying, 100 − x, by the price per ticket.)
b. Graph the expression from part a.
c. Find the number of unsold seats that will produce the maximum revenue.
d. What is the maximum revenue?
e. Some managers might be concerned about the empty seats, arguing that it doesn’t make economic sense to leave any seats empty. Write a few sentences explaining why this is not necessarily so.
ANSWER:
SOLUTION:
Step 1 of 6:
In this question, a charter flight charges a fare of $200 per person plus $4 per person for each unsold seat on the plane. The plane holds 100 passengers. Let represent the number of unsold seats. (a) Find an expression for the total revenue received for the flight . (b) Graph the expression from part (a). (c) Find the number of unsold seats that will produce the maximum revenue. (d) Find the maximum revenue. (e) Some managers might be concerned about the empty seats, arguing that it doesn’t make economic sense to leave any seats empty. Write a few sentences explaining why this is not necessarily so.
